ON A CONJECTURE OF WOOD

We show that there exists a locally compact separable metrizable space L such that C(0)(L), the Banach space of all continuous complex-valued functions vanishing at infinity with the supremum norm, is almost transitive. Due to a result of Greim and Rajagopalan [3], this implies the existence of a locally compact Hausdorff space L such that C(0)(L) is transitive, disproving a conjecture of Wood [9]. We totally owe our construction to a topological characterization due to Sanches [8].